I have found an attribution of this quote to a contemporary of Plato, Damon of Athens. Of course, that attribution may also be in error. Quadibloc (talk) 23:22, 25 May 2016 (UTC)

I have sorted this out. The misattribution to Plato leads to one to Damon of Oa, as Plato quotes Damon when he writes about music. Plato did write of the importance of music, although not in the words of Andrew Fletcher; he (Plato) came close, though, when he wrote: "musical styles never change without modifying the most important political laws too, as Damon says and I believe him". Quadibloc (talk) 23:30, 25 May 2016 (UTC)